In precision medicine applications, the rewards are often defined in the context of survival outcomes, such as mean survival time or survival probabilities, which pose unique challenges. For survival outcomes, the failure time is often censored, and any approach should take into account the missing information. Several methods have been developed for this purpose, for example, redistribution of the failure probability as in the Kaplan-Meier [1]} and [2]} or inverse probability weighting [3]}, [4]}, [5]}, [6]}. Further, the treatment timing may not be fixed and may even depend on a patient's status or previous treatments having association with the failure time. In such scenarios, the three events at each stage are failure, proceeding to the next treatment, and censoring, which can be restated in a competing risks framework, in which the three dependent events compete and only the earliest event is observed. However, the full joint distribution of the events is not identifiable without knowledge of their dependence structure [7]}. Thus, the dependency between the events needs to be carefully considered.
For example, a cancer patient whose physical condition has improved
has a longer expected survival time and at the same time may want to take another round of chemotherapy earlier than expected. If this is the case, the survival time and the treatment time have a negative association.
